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# Left-orderable Fundamental Group and Dehn Surgery on the Knot $5_2$

Published:2013-08-09
Printed: Jun 2014
• Ryoto Hakamata,
Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
• Masakazu Teragaito,
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
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## Abstract

We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is the two-bridge knot corresponding to the rational number $3/7$, has left-orderable fundamental group if the slope $r$ satisfies $0\le r \le 4$.
 Keywords: left-ordering, Dehn surgery
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 06F15 - Ordered groups [See also 20F60]